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Topic: Mathematical model

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Model (abstract)

Mathematical models in physics

Model theory

Simulation

Computer simulation

Autoregressive conditional heteroskedasticity

Applied mathematics

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Hyperbolic geometry

Binomial options model

Model organism

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	Mathematical model - Wikipedia, the free encyclopedia
		Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively.
		Note this model assumes the particle is a point mass, which is certainly known to be false in many cases we use this model, for example, as a model of planetary motion.
		Mathematical modelling problems are often classified into fl box or white box models, according to how much a priori information is available of the system.
	en.wikipedia.org /wiki/Mathematical_model (1749 words)

	2.3.5 MATHEMATICAL MODELING (Site not responding. Last check: 2007-10-20)
		Mathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon.
		Mathematical models of time dependent processes can be split into two categories depending on how the time variable is to be treated.
		Develop a mathematical model that will determine the rotational rate of the station as a function of the radius of the station (distance from the center of rotation) and the desired artificial gravitational force.
	www.aspire.cs.uah.edu /textbook/projdev2006.html (876 words)

	[No title]
		Mathematics is studied because it is a rich and interesting discipline, because it provides a set of ideas and tools that are effective in solving problems which arise in other fields, and because it provides concepts useful in theoretical studies in other fields.
		Given a situation in a field other than mathematics or in everyday life, mathematical model building is the activity that begins with the situation and formulates a precise mathematical problem whose solution, or analysis in the case of theory construction, enables us to better understand the original situation.
		Mathematical modeling usually begins with a situation in the real world, sometimes in the relatively controlled conditions of a laboratory and sometimes in the much less completely understood environment of meadows and forests, offices and factories, and everyday life.
	www.indiana.edu /~hmathmod/modeling-intro.html (1424 words)

	Surface Evolver Documentation - Mathematical model (Site not responding. Last check: 2007-10-20)
		As a generalization of the torus model, you may declare the domain to be the quotient space of R^n with respect to some symmetry group.
		This is the underlying symmetry for the torus model.
		This is a symmetry group on the Klein model of hyperbolic space whose quotient group is a genus 2 hyperbolic manifold.
	www.susqu.edu /brakke/evolver/html/model.htm (4292 words)

	Model - Wikipedia, the free encyclopedia
		Computer model, a computer program which attempts to simulate an abstract model of a particular system, usually builds upon a mathematical model
		Model (art), a person who poses for purposes of art, for example in art school (often known as an artist's model)
		Model (person), a person whose occupation is to display products, eg.
	en.wikipedia.org /wiki/Model (350 words)

	[No title]
		Mathematical models are frequently used to describe the state of a physical system as the system evolves in time.
		A common notational convention in mathematical modeling is to use variables of an opposite case to denote the mathematical model approximations of physical quantities.
		The model is based on the assumptions that (1) air resistance is negligible and (2) acceleration due to gravity is constant.
	www.krellinst.org /AiS/textbook/unit2/rock.html (1944 words)

	Model Theory
		Model theory began with the study of formal languages and their interpretations, and of the kinds of classification that a particular formal language can make.
		But in a broader sense, model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures, with Alfred Tarski's truth definition as a paradigm.
		These are very different senses of ‘model’ from that in model theory: the ‘model’ of the phenomenon or the system is not a structure but a theory, often in a formal language.
	plato.stanford.edu /entries/model-theory (6225 words)

	Different Models for Different Purposes
		Models are constructed to emphasize the visibility of the characteristics that are to be studied.
		Logical arguments can be made about the statements in the mathematical model; the conclusions about the mathematical statements can be translated to statements about what might be observed in the real world.
		Since deterministic models often provide good approximate predictions, and since they employ the well-studied tools of calculus and differential equations, they still are widely used in the physical as well as life and social sciences.
	www19.homepage.villanova.edu /alice.deanin/courses/Mat7310/models.htm (1133 words)

	Improved Nonlinear Mathematical Model of Viscoelasticity
		An improved nonlinear mathematical model is being developed for use in predicting the complex, time-varying stress-and-strain behaviors of viscoelastic materials.
		The development of this model is prompted by (1) the lack of success of older constitutive mathematical models that contain hereditary integrals of linear viscoelasticity (e.g., integrals that express current stresses in terms of histories of strains and of relaxation moduli) and (2) the need for a nonlinear model subject to efficient numerical implementation.
		Fitting this model to experimental data is expected to be much more straightforward than it is for older nonlinear mathematical models of viscoelasticity: the figure illustrates how this is so.
	www.nasatech.com /Briefs/Apr98/MFS28623.html (407 words)

	ARS \| Publication request: Description and Validation of a Mathematical Model of Varroa Mite (Varroa Destructor) and ...
		The model also predicts that economic threshold levels and the effectiveness of miticides in increasing colony survival are dependent on the geographic location of the colony and its effects on brood rearing.
		The model also predicts that economic threshold levels and the effectiveness of miticides in increasing colony survival are dependent on the geographic location of the colony and the yearly brood rearing cycle.
		The model predicts that spring applications of miticides are not as effective at prolonging colony survival as fall applications in temperate environments.
	www.ars.usda.gov /research/publications/publications.htm?SEQ_NO_115=148260 (497 words)

	Earth Atmosphere Model - English Units
		The model was developed from atmospheric measurements that were averaged and curve fit to produce the given equations.
		The particular model shown here was developed in the early sixties, and the curve fits are given for English units.
		The model has three zones with separate curve fits for the troposphere, the lower stratosphere, and the upper stratosphere.
	www.grc.nasa.gov /WWW/K-12/airplane/atmos.html (613 words)

	New mathematical model better describes transistor behavior
		Penn State and Philips researchers have merged the best features of their respective approaches to produce a new mathematical model that describes the behavior of the MOS transistor in a wide class of integrated circuits found in the majority of electronic devices from computers to digital watches to communications systems.
		The key variable in the PSP model is surface potential at the interface between the silicon and silicon dioxide in the transistor.
		Models, such as PSP, which describe transistors in a mathematical way, are used in circuit simulators.
	www.eurekalert.org /pub_releases/2005-05/ps-nmm051005.php (528 words)

	[No title]
		In a mathematical model, the state variables or field variables are quantities that characterize the behavior of the physical system.
		A mathematical model for a spring-mass system can be developed from Newton's 2nd Law of motion and the definitions of velocity and momentum.
		To continue our development of a mathematical model of the spring-mass system, consider an object of mass m that is moving in a straight line.
	www.krellinst.org /AiS/textbook/unit2/spring.html (1972 words)

	Ivars Peterson's MathTrek - Knot Divided in Snow
		Mathematical forms are no longer unusual sights at the annual International Snow Sculpture Championships in Breckenridge, Colo. For 7 years, mathematician Stan Wagon of Macalester College in St. Paul, Minn., and his team have carved huge blocks of snow into graceful geometric shapes.
		You can make a model of one by joining the two ends of a long strip of paper after giving one end a 180-degree (or half) twist.
		Interestingly, the winning entry, from a Tennessee team, also featured a mathematical shape—an intricate rendition of the shell of a nautilus (see http://www.gobreckevents.com/isscsnowsculpture.htm).
	www.maa.org /mathland/mathtrek_02_07_05.html (647 words)

	A Mathematical Model of the Electrophysiological Alterations in Rat Ventricular Myocytes in Type-I Diabetes -- Pandit ...
		A Mathematical Model of the Electrophysiological Alterations in Rat Ventricular Myocytes in Type-I Diabetes -- Pandit et al.
		A Mathematical Model of the Electrophysiological Alterations in Rat Ventricular Myocytes in Type-I Diabetes
		Kv4.2, Kv4.3, and Kv2.1 are downregulated in this acute model
	www.biophysj.org /cgi/content/full/84/2/832 (5025 words)

	gizmag Article: Mathematical model accurately predicts which couples will divorce (Site not responding. Last check: 2007-10-20)
		There are no general laws of human relationships as there are for physics, but a leading marital researcher and group of applied mathematicians have teamed up to create a mathematical model that predicts which couples will divorce with astonishing accuracy.
		The mathematical model charts this interaction into what the researchers call a "Dow-Jones Industrial Average for marital conversation." "When the masters of marriage are talking about something important, they may be arguing, but they are also laughing and teasing and there are signs of affection because they have made emotional connections," Gottman said.
		For example, the model permits them to see what happens if a behavior changes, say a husband allowing himself to be influenced by his wife, and how that increases the number of positive interactions.
	www.gizmo.com.au /public/News/news.asp?articleid=2605 (770 words)

	EID V3N3 Using a Mathematical Model to Evaluate the Efficacy of TB Control Measures
		The model describes how a person can become infected by staying in a room where a source of airborne infection and an air disinfection device are present.
		Our model is based on Wells' experiments and postulates and includes the Riley/Murphy/Riley model as a particular case (24).
		Our mathematical model indicates that a certain number of persons exposed to a source of TB infection will be infected in spite of all precautions.
	www.cdc.gov /ncidod/EID/vol3no3/nucci.htm (3360 words)

	Cornell News: mathematical model of language death (Site not responding. Last check: 2007-10-20)
		Others, they say, have used mathematical modeling to study the evolution of grammar, syntax and other structural features, but they believe this is the first attempt to quantify competition between languages.
		When population figures are plugged in, the model produces a family of curves depending on the value assigned to status, and in each case one of the curves agreed with the published data on language decline.
		An example of a situation where the model doesn't work is in the persistence of Spanish in the United States, which he attributes to a constant resupply of native speakers.
	www.news.cornell.edu /releases/Sept03/language_death.ws.html (573 words)

	The Minstrel's Song: a Mathematical Model
		This model represents a mathematician's second attempt at making a mathematical model, and as such is very detailed, complex, and at times hard to keep track of.
		If you are not a heavy gamer, and are not used to complex mathematical models, I strongly suggest that you use this simpler model.
		It is the wide concensus of gamers that r-o-l-e-play is infinitely superior to r-o-l-l-play; this model is a miniscule thing which governs a timy part of play, and calls for contrainte in use.
	alumni.imsa.edu /~jhayward/model.dice.html (10985 words)

	Of A New Mathematical Model, Nature, Nurture And IQ
		The model also examines the power of the "social multiplier" effect to shape individual IQ in accordance with the average IQs of one's social circle and society at large.
		The model permits researchers to sidestep the seemingly insoluble debate over the exact contributions of genetics and environment, by viewing the two as contributing differently to a process that itself changes depending on a person's age and circumstances.
		The model also helps account for how early education programs rapidly raise the IQ scores of low-income children -- again, while they are in them -- with slow decays after they leave.
	unisci.com /stories/20012/0417014.htm (946 words)

	Applications of Math Syllabus (Site not responding. Last check: 2007-10-20)
		The discussion will center on the types of mathematical models and their classification in terms of deterministic versus stochastic and discrete versus continuous.
		Model validation with newly acquired data is discussed and used to adjust the model in the iterative approach.
		Models used in the physical, social, and life sciences will be introduced and the mathematics used in the analysis of these models will be discussed.
	www.rowan.edu /math/Syllbabi/UND.COURSES/_AppofMath.html (312 words)

	The Chronicle: 4/25/2003: Every Unhappy Family Has Its Own Bilinear Influence Function
		The models presented in the book, he says, offer insights into the heaven and hell of couplehood that he would never have found by sifting through his data with standard linear statistical tools.
		What the students were modeling in that lounge was not "marriage" per se, but the dynamics of marital conversations.
		Gottman, "The mathematical model draws you to doing certain types of experiments that you wouldn't have thought of doing without the model." The nonlinear equations suggest particular ways for therapists to teach distressed couples to snap out of it when they find themselves in a negative steady state.
	chronicle.com /free/v49/i33/33a01401.htm (2418 words)

	It all adds up: Mathematical model shows which couples will divorce
		Murray, who is an emeritus professor of applied mathematics at the UW and Oxford University, agreed, noting that a lot of people are phobic about mathematics and that psychology has not been exposed to models.
		The model was developed using data collected from hundreds of videotaped conversations between couples in Gottman's laboratory.
		Gottman, Murray and Swanson, who is a UW research assistant professor of pathology and adjunct research assistant professor of applied mathematics, also will participate in an AAAAS symposium on the science of love and marriage that runs from 11 a.m.
	www.eurekalert.org /pub_releases/2004-02/uow-iaa020904.php (675 words)

	A Mathematical Model of the Mating Preferences of H. Sapiens
		A Mathematical Model of the Mating Preferences of H. Sapiens
		A Mathematical Model of the Mating Preferences of H.
		Our model also fails to take into account varying degrees of homosexual tendancies among the individuals of the population.
	endeavor.med.nyu.edu /~strone01/matingmodel.html (719 words)

	2005 Cy Young Winners Correctly Predicted by Mathematical Model
		A mathematical model for predicting the Cy Young award voting results yielded both of the 2005 winners, Chris Carpenter of the St. Louis Cardinals (National League) and Bartolo Colon of the Los Angeles Angels of Anaheim (American League).
		However, the model's inventors made a small human error they would later regret: Prior to the awards, they overrode the model's American League prediction by saying that New York Yankees reliever Mariano Rivera would win the title, rather than the model's choice of Bartolo Colon, who turned out to be the correct pick.
		The model, which is designed to analyze starting pitchers only, is currently not equipped to evaluate relief pitchers, who occasionally win the award.
	aip.org /isns/reports/2005/020.html (379 words)

	Chessays - Pavle Bidev - Chess - a Mathematical Model of the Cosmos?
		Chessays - Pavle Bidev - Chess - a Mathematical Model of the Cosmos?
		If he wants to captivate a woman, he makes her a small figure of wax, fancies that it is identical to the original, speaks the formulas of entreaty, piercing her heart with a needle.
		He made for himself a small model of the Universe in strict correspondence with his conception of the world.
	www.goddesschess.com /chessays/bidev1.html (6668 words)

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